Mathematics, mathematics education and computer programming.

Formula Triangles and an Odd Misconception

Formula triangles are quite prevalent in the UK (I’m not about elsewhere to be honest) – especially in science lessons and when right angled triangle trigonometry is taught. A typical example is the following for the relationship between speed, distance and time:

I’ve expressed my dislike (hatred is perhaps too strong a word) of formula triangles on Twitter before and others have written about them including Stephen Cavadino. Like Stephen my main reason for not being a fan of them is that they are usually introduced as a “trick” for use in particular situations with no reference to the underlying mathematics.

One of my students when looking at rearranging formulae was asked to make t the subject of an equation and drew a formula triangle as shown below (I’ve re-written it!)

When I asked why they had drawn a formula triangle they responded “well there are 3 terms so it’s a formula triangle question”. I’ve never seen this misconception before, I guess it is maybe down to formula triangles being used only for 3 term formulae and then this link becoming solidified in the student.

When I probed a bit further and asked things like “why have you picked 4a to be on the top” after a while they realised their mistake. I can’t help thinking that this wouldn’t have come about if they had never seen a formula triangle and instead had just had plenty of opportunity to practice rearranging formulae.